### On Solving Fuzzy Rough Linear Fractional Programming Problem

El-Saeed Ammar, Mohamed Muamer
International Research Journal of Engineering and Technology   unpublished
In this paper, introduce algorithm for solving fuzzy rough linear fractional programming (FRLFP) problem. All variables and coefficients of the objective function and constraints are fuzzy rough number. The FRLFP problem can be reduced as to the multi objective fuzzy linear fractional programming (FLFP) problems, where all variables and coefficients of the objective function and constraint are fuzzy number. Further, using the decomposition algorithm to obtain an optimal fuzzy rough solution. A
more » ... rough solution. A numerical example is given for the sake of illustration. Key Words:Triangular fuzzy number, Fuzzy rough interval, Multi objective linear fractional programming 1.INTRODUCTION We need to fractional linear programming in many real-world problems such as production and financial planning and institutional planning and return on investment, and others. Multi objective Linear fractional programming problems useful targets in production and financial planning and return on investment. Charnes and Cooper, Used variable transformation method to solve linear fractional programming problems [1]. Tantawy, Proposes a new method for solving linear fractional programming problems [2]. Jayalakshmi and Pandian, Proposed a new method namely, denominator objective restriction method for finding an optimal solution to linear fractional programming problems [3]. Moumita and De, Study of the fully fuzzy linear fractional programming problem using graded mean integration representation method [4]. Ezzati et al, Used a new algorithm to solve fully fuzzy linear programming problems using the multi objective linear programming problem [5]. Haifang et al, Solving a fully fuzzy linear programming problem through compromise programming [6].Pawlak, Used a rough set theory a new mathematical approach to imperfect knowledge [7]. Kryskiewice, Used a rough set theory to incomplete has found many interesting applications [8]. Pal, The rough set approach seems to be of fundamental importance to cognitive sciences, especially in the areas of machine learning, decision analysis, and expert systems [9]. Pawlak, Rough set theory, introduced by the author, expresses vagueness, not by means of membership, but employing a boundary region of a set. The theory of rough set deals with the approximation of an arbitrary subset of a universe by two definable or observable subsets called lower and upper approximations [10]. Tsumoto, Used the concept of lower and upper approximation in rough sets theory, knowledge hidden in information systems may be unraveled and expressed in the form of decision rules [11]. Lu and Huang, The concept of rough interval will be introduced to represent dual uncertain information of many parameters, and the associated solution method will be presented to solve rough interval fuzzy linear programming problems [12]. In this paper, we propose algorithm for solve fuzzy rough linear fractional programming problem where all variables and coefficients are fuzzy rough number. Use the decomposition to the fully fuzzy linear fractional programming problem for obtaining an optimal fuzzy rough solution, based on the variable transformation method.